The EPR Paradox

The EPR paradox is an early and influential critique leveled against quantum mechanics. Albert Einstein and his colleagues Boris Podolsky and Nathan Rosen (known collectively as EPR) designed a thought experiment intended to reveal what they believed to be inadequacies of quantum mechanics. To that end they pointed to a consequence of quantum mechanics that its supporters had not noticed. According to quantum mechanics, a single system has its own wave function, its own unitary quantum-theoretical description. If such a single system can be transformed into two individual systems, doing so does not create two wave functions. Instead, theory indicates that each system shares a single wave function.

Today, we call such two individual subsystems entangled. It was known from experiments that outcome of an experiment sometimes cannot be uniquely predicted. Example of such indeterminacy can be seen when a beam of light is incident on half-silvered mirror. One half of the mean will reflect, the other will pass. But what happens when we keep decreasing intensity of the beam, so that only one photon is in transit at any time? Half of the photons will pass and other half will reflect. Even if we ‘prepare’ the photons by passing them through a polarizer, there will always be an experiment the result of which could not be predicted with certainty. The routine explanation of this effect was at that time provided by the Heisenberg’s uncertainty principle. The physical quantities do come in pairs which are called Conjugate quantities. Example of such a conjugate pair are position and momentum of a particle, or component of spin measured around different axes. When one quantity was measured, and became determined, the conjugated quantity became indeterminate.

Heisenberg explained this by disturbance caused by measurement. The EPR paper written in 1936 has shown that this explanation is inadequate. They considered two entangled particles, let’s call them A and B, and pointed out measuring a quantity of a particle A will cause the conjugated quantity of particle B to become undetermined, even if there was no contact, no classical disturbance. Heisenberg’s principle was an attempt to provide a classical explanation of a quantum effect we call non-locality. There were two possible explanations. Either there was some interaction between the particle, even though they were separated or the information about the outcome of all possible measurements was already present in both particles. EPR authors preferred the second explanation according which that information was encoded in some ‘hidden parameters’. The first explanation, that effect propagated instantly, at a distance, was (and is) in conflict with theory of relativity.

Their reasoning in the paper was correct and the Heisenberg principle now has only historical significance, even though it persist in popular books and popular culture. However as later experiments and Bell’s theorem demonstrated their preferred explanation was not possible. They then concluded that quantum mechanics was incomplete since in it’s formalism there was no space for such hidden parameters. They would both be determinate values, not just one of them as indicated by quantum mechanics. If the two values of the remote, undisturbed, system were real, then they must have been real all along and not determined by the act of measurement. The act of measurement might well disturb and change subsequent values of the system measured, but that fact did not deny that there must have been something real there to be measured all along. In short, they gave reason to believe that the second, undisturbed, system had a real and definite position, and a real and definite momentum, and that therefore the first system must also have had a real and definite position, and a real and definite momentum waiting there for the experimenter to disturb and change. However, quantum mechanics could not provide a theoretical description or prediction of these values, and so must be held to be incomplete.

Implications for quantum mechanics

Most physicists today believe that quantum mechanics is correct, and that the EPR paradox is a “paradox” only because classical intuitions do not correspond to physical reality. How EPR is interpreted regarding locality depends on the interpretation of quantum mechanics one uses. In the Copenhagen interpretation, it is usually understood that instantaneous wavefunction collapse does occur. However, the view that there is no causal instantaneous effect has also been proposed within the Copenhagen interpretation: in this alternate view, measurement affects our ability to define (and measure) quantities in the physical system, not the system itself. In the many-worlds interpretation locality is strictly preserved, since the effects of operations such as measurement affect only the state of the particle that is measured. However, the results of the measurement are not unique — every possible result is obtained.

The EPR paradox has deepened our understanding of quantum mechanics by exposing the fundamentally non-classical characteristics of the measurement process. Prior to the publication of the EPR paper, a measurement was often visualized as a physical disturbance inflicted directly upon the measured system. For instance, when measuring the position of an electron, one imagines shining a light on it, thus disturbing the electron and producing the quantum mechanical uncertainties in its position. Such explanations, which are still encountered in popular expositions of quantum mechanics, are debunked by the EPR paradox, which shows that a “measurement” can be performed on a particle without disturbing it directly, by performing a measurement on a distant entangled particle. In fact, Yakir Aharonov and his collaborators have developed a whole theory of so-called Weak measurement.

Technologies relying on quantum entanglement are now being developed. In quantum cryptography, entangled particles are used to transmit signals that cannot be eavesdropped upon without leaving a trace. In quantum computation, entangled quantum states are used to perform computations in parallel, which may allow certain calculations to be performed much more quickly than they ever could be with classical computers.